Question

Assertion A parallel plate capacitor is connected across battery through a key. A dielectric slab of dielectric constant $K$ is introduced between the plates. The energy which is stored becomes $K$ times.
Reason The surface density of charge on the plate remains constant or unchanged.

• A. Both assertion and reason are true and reason is the correct explanation of assertion
• B. Both assertion and reason are true but reason is not the correct explanation of assertion
• C. Assertion is true but reason is false
• D. Both Assertion and reason are false

Answer 1

Answer: (C)

If a dielectric slab of dielectric constant $K$ is filled in between
the plates of a condenser while charging it, the potential
difference between the plates does not change but the
capacity becomes $K$ times, therefore $V' = V , C' = KC$
Energy stored in the capacitor
$U' = \frac{1}{2} C'V'^2$
$= \frac{1}{2}(KC)(V^2)$
$= [\frac{1}{2}CV^2] K$
$ = KU$
Thus, energy stored becomes $K$ times. Surface charge density
$\sigma = \frac{q'}{A} = \frac{C' V'}{A} = \frac{KCV}{A}$
$= K \frac{q}{A} = K \sigma$